A force of 10 lb is inclined to the x-axis at 60 degrees. Find its horizontal and vertical components.

2 Answers

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The force F is inclined to the x axis at 60 degrees.

To find the the horizontal and vertical components.

Le the horizontal line be x axis and the vertical line be y axis.

Then resolving the force 10 lb along the horizontal line , we get:

Horizontal component = 10lb cos60 deg = 10*(1/2) = 5 lb along x axis.

The vertical component of 10 lb = 10lb sin60 = 10lb sin 60 = 10*(sqrt3)/2 = 5 sqrt3 lb = 8.66lb approx. along y axis.

Therefore the horizontal and the vertical components of the 10 lb force are 5lb and 8.66lb respectively. 

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since the force is a vector, it's components are the projections of the resultant force of 10 lb. on x and y axis.

The vector of force is making a 60 degrees angle to x axis.

To compute it's x axis component, we'll apply cosine function.

cos 60 = Fx/F

Fx = F*cos 60

Fx = 10*(1/2)

Fx = 5 lb.

To compute the component on y axis, we'll apply sine function:

sin 60 = Fy/F

Fy = F*sin 60

Fy = 10*(sqrt3/2)

Fy = 5*sqrt3

Fy = 8.66 lb.